Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematic...Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematical advance in the description of physical phenomena described by the second derivative operator associated with a divergent interaction potential and, being analytical, guarantee the optimal interpretation of such phenomena.展开更多
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollo...Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.展开更多
In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum Liu-Tesehe （BLT）...This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum Liu-Tesehe （BLT） equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent.展开更多
The dynamical behaviour of the inorganic bromate oscillator catalyzed by manganese ions in the B-Z reaction is discussed, a three-variable nonlinear dynamical equations of the oscillation phenomena have been obtained,...The dynamical behaviour of the inorganic bromate oscillator catalyzed by manganese ions in the B-Z reaction is discussed, a three-variable nonlinear dynamical equations of the oscillation phenomena have been obtained, and an analytic solution and numerical results of the equations are given.展开更多
In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing ...In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.展开更多
In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience ...In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.展开更多
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surf...According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.展开更多
We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for ...We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.展开更多
Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the W...Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique. Firstly, without regard for elastic edge restraint, the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results. Therefore, it can be shown that the present method is valid. Secondly, three end-restraint cases （i.e., the left-end elastic restraints, the both-end elastic restraints, and the right-end elastic restraints） are proposed to reduce the vibration of floating plates, in which the spring is used to connect the sea bottom and the floating plate＇ s left （ or right ） edge. The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed. Moreover, the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.展开更多
Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a cont...Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a continuous map, and f|(D m)° is analytic}. For H∈ A(D m,C)(m≥2), f∈A(D,D) and z∈D, write Ψ H(f)(z)=H(z,f(z),...,f m-1(z)). Suppose F,G∈A(D 2n+1,C), and H k,K k∈A(D k,C), k=2,...,n. In this paper, the system of functional equations F(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0 G(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0(z∈D) is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D) are given.展开更多
The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely ana...The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.展开更多
The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible vi...The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.展开更多
By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions ...By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.展开更多
This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV）...This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.展开更多
We study a forced variable-coefficient extended Korteweg-de Vries(KdV)equation in fluid dynamics with respect to internal solitary wave.Bäcklund transformations of the forced variable-coefficient extended KdV equ...We study a forced variable-coefficient extended Korteweg-de Vries(KdV)equation in fluid dynamics with respect to internal solitary wave.Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevéexpansion.When the variable coefficients are time-periodic,the wave function evolves periodically over time.Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations.One-parameter group transformations and one-parameter subgroup invariant solutions are presented.Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method.The consistent Riccati expansion(CRE)solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE.Interaction phenomenon between cnoidal waves and solitary waves can be observed.Besides,the interaction waveform changes with the parameters.When the variable parameters are functions of time,the interaction waveform will be not regular and smooth.展开更多
With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion a...With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.展开更多
Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency f...Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.展开更多
On the basis of a self-similar solution as well as of the assumption of the 'Transserse Motion',a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this t...On the basis of a self-similar solution as well as of the assumption of the 'Transserse Motion',a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this theory, the problem concerned can he put into a universal system of O.D Eqs .which can be integrated manerically in adyance展开更多
B. Riemann furnished the general solution of simple waves in 1860[1] But it is difficult to find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial c...B. Riemann furnished the general solution of simple waves in 1860[1] But it is difficult to find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial conditions. For this reason it is inconvenient to probe into the characteristics of concrete problems. In this paper the analytic solutions of simple waves are afforded according to the geometric theory of quasi-linear partial differential equation, and they are determined with boundary or initial conditions. By using these solutions the specific properties of certain flows are discussed and novel results are obtained.展开更多
文摘Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematical advance in the description of physical phenomena described by the second derivative operator associated with a divergent interaction potential and, being analytical, guarantee the optimal interpretation of such phenomena.
基金supported by National Natural Science Foundation of China (Grant No. 50875230)
文摘Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
基金Project supported by the China Postdoctoral Science Foundation(Grant No 20080431399)the National Natural Science Foundation of China (Grant No 60572135)
文摘This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum Liu-Tesehe （BLT） equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent.
基金Supported by the Natural Science Foundation of Liaoning Educational Committee(No.9970311012).
文摘The dynamical behaviour of the inorganic bromate oscillator catalyzed by manganese ions in the B-Z reaction is discussed, a three-variable nonlinear dynamical equations of the oscillation phenomena have been obtained, and an analytic solution and numerical results of the equations are given.
基金the financial support of National Board forHigher Mathematics (NBHM),DAE,Mumbai,India for pursuing this workThe research of A. Alsaedi is partially supported by the Deanship of Scientific Research (DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.
文摘In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.
文摘According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.
基金supported by National Natural Science Foundation of China(11101295)
文摘We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.
基金This work was supported by the National Natural Science Foundation of China(Grant No.19972018)Distin-guished Young Scholar Science Foundation of Heilongjiang Province of China.
文摘Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique. Firstly, without regard for elastic edge restraint, the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results. Therefore, it can be shown that the present method is valid. Secondly, three end-restraint cases （i.e., the left-end elastic restraints, the both-end elastic restraints, and the right-end elastic restraints） are proposed to reduce the vibration of floating plates, in which the spring is used to connect the sea bottom and the floating plate＇ s left （ or right ） edge. The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed. Moreover, the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.
基金Supported by the National Natural Science Foundation of China (1 0 2 2 6 0 1 4) ,Guangxi Science Foun-dation (0 2 2 90 0 1 )
文摘Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a continuous map, and f|(D m)° is analytic}. For H∈ A(D m,C)(m≥2), f∈A(D,D) and z∈D, write Ψ H(f)(z)=H(z,f(z),...,f m-1(z)). Suppose F,G∈A(D 2n+1,C), and H k,K k∈A(D k,C), k=2,...,n. In this paper, the system of functional equations F(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0 G(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0(z∈D) is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D) are given.
基金supported by the National Natural Science Foundation of China under Grant No.10575140the Basic Research of Chongqing Education Committee under Grant No.KJ060813
文摘The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.
文摘The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.
文摘By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11775047,11775146,and 11865013).
文摘We study a forced variable-coefficient extended Korteweg-de Vries(KdV)equation in fluid dynamics with respect to internal solitary wave.Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevéexpansion.When the variable coefficients are time-periodic,the wave function evolves periodically over time.Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations.One-parameter group transformations and one-parameter subgroup invariant solutions are presented.Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method.The consistent Riccati expansion(CRE)solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE.Interaction phenomenon between cnoidal waves and solitary waves can be observed.Besides,the interaction waveform changes with the parameters.When the variable parameters are functions of time,the interaction waveform will be not regular and smooth.
文摘With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.
基金Supported by the National Natural Science Foundation of China(10672022)
文摘Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.
文摘On the basis of a self-similar solution as well as of the assumption of the 'Transserse Motion',a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this theory, the problem concerned can he put into a universal system of O.D Eqs .which can be integrated manerically in adyance
文摘B. Riemann furnished the general solution of simple waves in 1860[1] But it is difficult to find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial conditions. For this reason it is inconvenient to probe into the characteristics of concrete problems. In this paper the analytic solutions of simple waves are afforded according to the geometric theory of quasi-linear partial differential equation, and they are determined with boundary or initial conditions. By using these solutions the specific properties of certain flows are discussed and novel results are obtained.
